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    利用分位数回归模拟人工樟子松树干干形

    Modeling stem taper profile for Pinus sylvestris plantations using nonlinear quantile regression

      摘要
    • 摘要:
      目的采用非线性分位数回归方法构建樟子松树干削度方程，并对比分析9个分位数（τ = 0.1，0.2，0.3，0.4，0.5，0.6，0.7，0.8，0.9）模型和传统的非线性回归削度方程的预测精度。
      方法以七台河市林业局金沙林场154株人工樟子松干形数据为研究对象，选取简单削度方程、分段削度方程和可变指数削度方程，利用非线性回归和非线性分位数回归方法构建樟子松树干削度方程。采用确定系数（R2）、平均误差（MAB）、相对误差（MPB）、均方根误差（RMSE）为统计指标对构建的削度方程进行对比分析。
      结果（1）在9个分位点（τ = 0.1，0.2，0.3，0.4，0.5，0.6，0.7，0.8，0.9）下的各削度方程都可以收敛，分位数回归方法可以灵活预测各分位点树干曲线的变化。（2）与非线性回归相比，基于中位数（τ = 0.5）时的各削度方程在拟合过程中表现最好，其中以可变指数削度方程表现最优。（3）检验结果也表明：相对于非线性回归的各削度方程，基于中位数（τ = 0.5）的简单削度模型的MAB和MPB均下降26.7%，RMSE下降19.9%；基于中位数（τ = 0.5）的分段削度方程和可变指数方程预测能力较强。（4）中位数回归的各削度方程在树干大部分的预测能力都优于相应的非线性削度方程。
      结论分位数回归方法是一种稳健的建模方式，基于中位数（τ = 0.5）的可变指数削度方程的预测精度最高，适合该区域樟子松树干干形的预测。

       

      Abstract:
      ObjectiveThe aim of this study was to develop stem taper equation for Pinus sylvestris based on quantile regression, and the prediction accuracy of the nine quantiles (τ = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) and the traditional nonlinear regression stem taper equations was compared and analyzed.
      MethodThe stem taper data of 154 Pinus sylvestris plantations in Jinsha Forest Farm of Qitaihe Forestry Bureau was taken as the research object. The single, segmented and variable form taper equations were selected, and the nonlinear quantile regression method was used to construct the stem taper equations of Pinus sylvestris. The performance of all constructed stem taper equations was compared and analyzed by these evaluation statistics: coefficient of determination (R2), mean absolute bias (MAB), root mean square error (RMSE), mean percentage of bias (MPB).
      Result(1) The results showed that the stem taper equations could converge at 9 quantiles (τ = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9), respectively. Quantile regression method can flexibly predict changes in taper curve of each quantile. (2) Compared with the nonlinear regression, the stem taper equations based on the median (τ = 0.5) perform best during the fitting process. The best performance was obtained for the variable exponential equation. (3) The validation results also showed that compared with the nonlinear regression equations, the MAB and MPB of the single taper equation based on the median (τ = 0.5) both decreased by 26.7% and the RMSE decreased by 19.9%. The segmented equation and the variable form equation based on the median (τ = 0.5) showed the better prediction ability. (4) The prediction equations of the median regression are better than the corresponding nonlinear equations for the most stem sections.
      ConclusionQuantile regression method is a robust modeling method, the variable exponential equation based on the median (τ = 0.5) shows more prediction precision. It is suitable for the prediction of stem taper for Pinus sylvestris in this region.

       

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